Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 meters cubed. Yolanda found the volume of the sphere.

A sphere with height h and radius r. A cylinder with height h and radius r.

Her work is shown below.

V = four-thirds (8) cubed. V = four-thirds (512). V = StartFraction 2,048 Over 3 EndFraction meters cubed.

What is Yolanda’s error?
Yolanda should have found the volume by multiplying 8 by Two-thirds.
Yolanda should have found the volume by multiplying 8 by Four-thirds.
Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed.
Yolanda should have found the volume with the formula V = two-thirds (8) cubed.

Answer 1

we know that

the height of cylinder is equal to the diameter of sphere

so

h=2*r------> equation 1

volume of cylinder=pi*r²*h

volume=8 m³

substitute equation 1 in the formula of volume

8=pi*r²*(2*r)------> 8=2*pi*r³-----> equation 2

find the volume of a sphere

volume sphere=(4/3)*pi*r³-----> (2/3)*[2*pi*r³]

substitute the equation 2 in the formula of volume

volume sphere=(2/3)*[8]----> 16/3 m³

the answer is

Yolanda should have found the volume by multiplying 8 by 2/3.

Answer 2

Yolanda should have found the volume by multiplying 8 by 2/3.

Explanation: